rule of infinite induction

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• Rule of inference — In logic, a rule of inference (also called a transformation rule) is a function from sets of formulae to formulae. The argument is called the premise set (or simply premises ) and the value the conclusion . They can also be viewed as relations… …   Wikipedia

• Mathematical induction — can be informally illustrated by reference to the sequential effect of falling dominoes. Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers (positive… …   Wikipedia

• Invalid proof — In mathematics, there are a variety of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle. These fallacies are normally regarded as mere curiosities, but can be used… …   Wikipedia

• Surreal number — In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share… …   Wikipedia

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• Spinoza: metaphysics and knowledge — G.H.R.Parkinson The philosophical writings of Spinoza are notoriously obscure, and they have been interpreted in many ways. Some interpreters see Spinoza as (in the words of a contemporary)1 ‘the reformer of the new [sc. Cartesian] philosophy’.… …   History of philosophy

• Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …   Wikipedia

• Occam's razor — For the aerial theatre company, see Ockham s Razor Theatre Company. It is possible to describe the other planets in the solar system as revolving around the Earth, but that explanation is unnecessarily complex compared to the modern consensus… …   Wikipedia

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• Mathematical proof — In mathematics, a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true.[1][2] Proofs are obtained from deductive reasoning, rather than from inductive or empirical… …   Wikipedia

• set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium